There are a bunch of line patterns loaded with Illustrator by default (Open Swatch Library → Patterns → Basic Graphics → Basic Graphics Lines).
You can use them as a second fill using the appearance panel and use blending etc to get the effect you want. You can add a Transform effect to that specific fill (make sure to check "Transform Patterns") to get the rotation & scale you want:
...and the same with a different blending mode:
If the default line patterns don't work for you then you can, of course, make your own pattern; which should be as easy as creating a small section of the lines you want (you could do it with a single line if you really wanted to) and dragging them to the Swatches panel, then double-clicking to enter the pattern editor: